New anisotropic a priori error estimates

We prove a priori anisotropic estimates for the L-2 and H-1 interpolation e rror on linear finite elements. The full information about the mapping from a reference element is employed to separate the contribution to the elemen tal error coming from different directions. This new H-1 error estimate doe s not require the "maximal angle condition". The analysis has been carried out for the 2D case, but may be extended to three dimensions. Numerical exp eriments have been carried out to test our theoretical results.